課程資料
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2184 線性代數
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開課學期：1091
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開課班級：
應數系 2B
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授課教師：何志昌
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必修
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學年課
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學分數：3.0
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大義 0406 星期三 08:10-11:00
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2184 LINEAR ALGEBRA
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2020 Fall
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Department of Applied Mathematics 2B
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Professor：HO, CHIH-CHANG
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Required
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Full Year
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Credits:
3.0
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Da Yi 0406 Wednesday 08:10-11:00
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發展願景
傳揚中華文化，促進跨領域創新，與時精進，邁向國際
It is our objective to promote Chinese culture, enhance cross-disciplinary innovation, seek constant advancement, and embrace global community.
辦學宗旨
秉承質樸堅毅校訓，承東西之道統，集中外之精華，研究高深學術, 培養專業人才，服務社會，致力中華文化之發揚, 促進國家發展.
Based on our motto—“Temperament, Simplicity, Strength, and Tenacity,” “inheriting the merits of the East and the West” and “absorbing the essence of Chinese and foreign cultures,” we make it our mission to pursue advanced research, develop professional talents, serve the society, promote Chinese culture and support national development.
校教育目標
校基本素養
校核心能力
院教育目標
奠定自然科學基礎培養後續學習能力
強化理論與實務並重的多元課程
推動跨領域學習
促進國際化教學提升學生競爭力
院核心能力
自然科學知識的能力
理論與實務結合的能力
國際化與團隊溝通合作的能力
多元整合的能力
系教育目標
訓練學生具備紮實的數學基本能力
依興趣選擇應用數學學群，統計科學學群，或計算機科學學群
兼顧理論與實務，讓學生得以繼續升學或直接就業
系核心能力
具備基礎科學知識能力
具計算、分析、演算法與證明等能力
使用數學或套裝軟體求解問題能力
具備系統性分析、解釋結果與表達溝通能力
課程目標
瞭解矩陣的概念，基本的運算、向量空間、線性變換、特徵值的意義和計算，及其在物理、工程、幾何、機率、管理、經濟等的應用。
Understand the concept of matrix, basic operations, vector space, linear transformation, meaning and calculation of eigenvalues, and their applications in physics, engineering, geometry, probability, management, economics, etc.
課程能力
具備基礎科學知識能力 (比重 15%)
具計算、分析、演算法與證明等能力 (比重 50%)
使用數學或套裝軟體求解問題能力 (比重 20%)
具備系統性分析、解釋結果與表達溝通能力 (比重 15%)
課程概述
本課程討論線性代數的理論及應用。內容包括2維,3維及n維向量,線性方程式,高斯消去法,矩陣,矩陣的運算,反矩陣的定義,矩陣的LU分解,轉置矩陣,排列矩陣,向量空間,矩陣的零核空間,矩陣的秩,列簡梯陣,Ax=b的全解,線性獨立,線性相依,基底,維數,4個子空間的維數,內積空間,垂直性,4個子空間的互相垂直問題,投影,最小差方,正交基底,Gram-Schmidt正交化過程,行列式的性質、餘因子、Cramer法則、反矩陣、特徵值、矩陣的對角化、對稱矩陣的對角化、正定矩陣、相似矩陣、奇異值分解、線性變換、線性變換的矩陣表示法、基底的變換、複數、Hermitian矩陣、單式矩陣、Jordan正則式。
The theory and applications of linear algebra will be discussed in this course. The topics of this course consist of 2,3 and n-dimensional vectors,linear equations,Gaussian Elimination,matrix,rules for matrix operations,definition of an inverse matrix,LU decomposition,transpose and permutation,vector spaces,
the null space of a matrix,the rank of a matrix,row reduced echelon form,the complete solution of Ax=b,linear independence,linear dependence,basis,dimension,dimension of the 4 spaces,inner product
spaces,orthogonality,orthogonality of the 4 subspaces,projections,least square approximations,orthogonal bases,Gram-Schmidt orthogonalization processes,the properties of determinant,permutation,
cofactors,Cramer’s rule,formula for inverse matrix,eigenvalues,diagonalizing a matrix, diagonalizing a symmetric matrix,positive definite matrices,similar matrices,singular value decomposition,linear transformation,the matrix representation of a
linear transformation,change of basis,complex n-dimensional vector
spaces,Hermitian and unitary matrices,diagonalization of Hermitian matrices,Jordan Canonical Form.
授課內容
教學目標：使同學熟悉線性代數的理論和應用
教學內容：本課程將介紹和討論下列主題:2維,3維及n維向量,線性方程式,高斯消去法,矩陣,矩陣的運算,反矩陣的定義,矩陣的LU分解,轉置矩陣,排列矩陣,向量空間,矩陣的零核空間,矩陣的秩,列簡梯陣,Ax=b的全解,線性獨立,線性相依,基底,維數,4個子空間的維數,內積空間,垂直性,4個子空間的互相垂直問題,投影,最小差方,正交基底,Gram-Schmidt正交化過程,行列式的性質,排列,餘因子,克拉瑪法則,反矩陣的公式,特徵值,矩陣的對角化,對稱矩陣的對角化,正定矩陣,相似矩陣,奇異值分解,線性變換,線性變換的矩陣表示法,基底轉換的矩陣表示法,複數的n維向量空間,Hermitian和單式矩陣, Hermitian矩陣的對角化,Jordan正則式
Objectives of the Course:
The purposes of this course are to develop the fundamental concepts of linear algebra, emphasizing those concepts which
are most important in applications.
Content of the Course:
In this course we will introduce and discuss the following topics:2,3 and n-dimensional vectors,linear equations,Gaussian Elimination,matrix,rules for matrix operations,definition of an inverse matrix,LU decomposition,transpose and permutation,vector spaces,
the null space of a matrix,the rank of a matrix,row reduced echelon form,the complete solution of Ax=b,linear independence,linear dependence,basis,dimension,dimension of the 4 spaces,inner product
spaces,orthogonality,orthogonality of the 4 subspaces,projections,least square approximations,orthogonal bases,Gram-Schmidt orthogonalization processes,the properties of determinant,permutation,
cofactors,Cramer’s rule,formula for inverse matrix,eigenvalues,diagonalizing a matrix, diagonalizing a symmetric matrix,positive definite matrices,similar matrices,singular value decomposition,linear transformation,the matrix representation of a
linear transformation,change of basis,complex n-dimensional vector
spaces,Hermitian and unitary matrices,diagonalization of Hermitian matrices,Jordan Canonical Form.
授課方式
講授(使用白板),討論
評量方式
上課用書
（師生應遵守智慧財產權及不得非法影印）
Introduction to Linear Algebra, fourth ed., by Gilbert Strang
參考書目
（師生應遵守智慧財產權及不得非法影印）
Elementary Linear Algebra, 8th edition, by Kolman and Hill
英文文獻 Integer Sequences :
An On-Line Version of the Encyclopedia of Integer Sequences
by N. J. A. Sloane
The Electronic Journal of Combinatorics, Volume 1 (1994)
課程需求
要考試
輔導時間
- 星期二 10:00-12:00
- 星期三 11:00-13:00
- 星期五 10:00-12:00
教師聯絡資訊
Email：hzc3@faculty.pccu.edu.tw
分機：25131
課程進度